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Nonlinear Optics

Autler-Townes Splitting and chi-2 Turing-Rolls in Microresonators

Dmitry V. Skryabin, Danila N. Puzyrev, V. V. Pankratov, Alberto Villois

Published Jan 1, 2021• 0 citations
Publisher

Abstract

We demonstrate that the generation of the sparse, i.e., Turing-pattern-like, frequency combs in chi-2 microresonators is explained by the four distinct signal-idler- pump photon energy conservation laws. The transformation of the usually unique three- photon energy conservation to the four conditions happens due to the effect analogous to the Autler-Townes splitting known in the strong photon-atom interaction.

DOI
10.1364/nlo.2021.nf1a.4

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We demonstrate that the generation of the sparse, i.e., Turing-pattern-like, frequency combs in chi-2 microresonators is explained by the four distinct signal-idler- pump photon energy conservation laws. The transformation of the usually unique three- photon energy conservation to the four conditions happens due to the effect analogous to the Autler-Townes splitting known in the strong photon-atom interaction.
We present a theory of frequency comb generation in high-Q ring microresonators with quadratic nonlinearity and normal dispersion and demonstrate that the naturally large difference of the repetition rates at the fundamental and second-harmonic frequencies supports a family of bright soliton frequency combs provided the parametric gain is moderated by tuning the index-matching parameter to exceed the repetition rate difference by a significant factor. This factor equals the sideband number associated with the high-order phase-matched sum-frequency process. The theoretical framework, i.e., the dressed-resonator method, to study the frequency conversion and comb generation is formulated by including the sum-frequency nonlinearity into the definition of the resonator spectrum. The Rabi splitting of the dressed frequencies leads to four distinct parametric down conversion conditions (signal-idler-pump photon energy conservation laws). The parametric instability tongues associated with the generation of the sparse, i.e., Turing-pattern-like, frequency combs with varying repetition rates are analyzed in detail. The sum-frequency matched sideband exhibits optical Pockels nonlinearity and strongly modified dispersion, which limit the soliton bandwidth and also play a distinct role in Turing comb generation. Our methodology and data highlight the analogy between the driven multimode resonators and the photon-atom interaction.
We consider a high-Q microresonator with chi-2 nonlinearity under conditions when the coupling rate between the sidebands around the pump and its second harmonic exceeds the damping rates, implying the strong coupling regime (SC). Using the dressed-resonator methodology, which is similar to the well-known theory of the two-levels atoms dressed by the optical fields, we demonstrate that this regime leads to the dominance of the reversible energy transfer between the sidebands over the non-reversible sideband growth due to parametric gain. This observation has allowed us to introduce and apply the cross-area concept of the polariton quasi-particles in the context of chi-2 ring-microresonators, and to use it to predict the modified spectral response of the resonator to the weak probe field. This response reveals the splitting of the bare-resonator resonances, avoided crossings, and Rabi dynamics. Using polaritons as the basis has also allowed us to derive a discrete sequence of the parametric thresholds for generation of sidebands of different orders. These thresholds form spectacular patterns in the parameter space defined by the detunings of the fundamental and 2 nd harmonic fields, Figs (a) and (b).
Whispering gallery mode optical microresonators represent a promising avenue for realizing optical analogs of coherent light–atom interactions, circumventing experimental complexities. All-optical analogs of Autler–Townes splitting have been widely demonstrated, harnessing coupled optical microresonators, also known as photonic molecules, wherein the strong coupling between resonant fields enables energy level splitting. Here, we report the characterizations of Autler–Townes splitting in waveguide-coupled microring dimers featuring mismatched sizes. By exploiting backscattering-induced coupling via Rayleigh and Mie scatterers in individual rings, high-order Autler–Townes splitting has been realized, yielding supermode hybridization in a multi-level system. Upon resonance detuning using an integrated phase shifter, intra-cavity coupling-induced splitting becomes almost indistinguishable at the zero-detuning point where the strong inter-cavity coupling counteracts the imbalance of backscattering strengths in individual rings. Through demonstrations on the maturing silicon photonics platform, our findings establish a framework of electrically tunable photonic molecules for coupling-mediated Autler–Townes splitting, offering promising prospects for on-chip signal generation and processing across classical and quantum regimes.
Quantum Kerr optical frequency combs are generated by pumping a high-Q microresonator with a continuous wave resonant laser. Below threshold, two pump photons are symmetrically up- and down-converted as twin photons via spontaneous four-wave mixing, thereby generating up to a hundred paired channels. Furthermore, these chipscale, high-dimensional and room-temperature systems are expected to play a major role in quantum engineering. However, their theoretical description is still unclear. Here, we present an explicit description of this quantum system via a frequency-bin state and its density operator, and explore the properties of the eigenkets.